In recent years, the relations between asymptotic symmetries and soft theorems have led to a promising candidate for flat holography: celestial holography. The central objects in this program are celestial amplitudes, which behave as correlation functions of primary operators in a putative conformal field theory: celestial CFT (CCFT). In this talk, we will first introduce some basics of celestial amplitudes and CCFT, including celestial operator product expansions (OPEs). We will describe one specific example, the celestial Liouville theory for Yang-Mills amplitudes based on work with Stieberger and Taylor. We will conclude with some open questions and future directions.